A Kleene-Stone algebra is a bounded distributive lattice with two unary operations that make it a Kleene and a Stone algebra. In this paper, we study the properties of the prime ideals in a Kleene-Stone algebra and ch...A Kleene-Stone algebra is a bounded distributive lattice with two unary operations that make it a Kleene and a Stone algebra. In this paper, we study the properties of the prime ideals in a Kleene-Stone algebra and characterize the class of Kleene-Stone algebras that are congruence permutable by means of the dual space of a Kleene-Stone algebra and then show that a finite Kleene-Stone algebra is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras.展开更多
基金Supported by the Science and Technology Project of Hubei Province (2006AA412C27)
文摘A Kleene-Stone algebra is a bounded distributive lattice with two unary operations that make it a Kleene and a Stone algebra. In this paper, we study the properties of the prime ideals in a Kleene-Stone algebra and characterize the class of Kleene-Stone algebras that are congruence permutable by means of the dual space of a Kleene-Stone algebra and then show that a finite Kleene-Stone algebra is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras.
